Harmonic and Applied Analysis From Radon Transforms to Machine Learning

Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science.  This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019.  Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers.  Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.  

Bartolucci, F., De Mari, F., Monti, M., Unitarization of the Horocyclic Radon Transform on Symmetric Spaces.- Maurer, A., Entropy and Concentration.-Alaifari, R., Ill-Posed Problems: From Linear to Non-Linear and Beyond.- Salzo, S., Villa, S., Proximal Gradient Methods for Machine Learning and Imaging.- De Vito, E., Rosasco, L., Rudi, A., Regularization: From Inverse Problems to Large Scale Machine Learning.